Toys R Us UK and electronics retailer Maplin have collapsed into administration, putting a total of 5,700 jobs at risk.
Toys R Us UK operates a store at Chesterfield's Spire Walk Retail Park.
Maplin has a shop at the town's Ravenside Retail Park.
Administrator Moorfields has been appointed at Toys R Us UK to conduct what it called an 'orderly wind-down of the store portfolio over the coming weeks'.
Simon Thomas, Moorfields partner, said: "All stores remain open until further notice and stock will be subject to clearance and special promotions.
"We're encouraging customers to redeem their gift cards and vouchers as soon as possible.
"We will make every effort to secure a buyer for all or part of the business."
Toys R Us UK has been searching for a buyer for the last month after weak Christmas trading which has left it with little hope of paying a £15million VAT bill due on Tuesday.
In December, the business announced plans to shut 26 of its 105 UK outlets.
Maplin bosses had been trying to find a buyer for the company but talks have failed.
Maplin stores will continue to trade through the administration process.